This article is mainly concerned how the double exponential formula for numerical integration was discovered and how it has been developed thereafter. For evaluation of I = ∫ 1 −1 f(x)dx H. Takahasi and M. Mori took advantage of the optimality of the trapezoidal formula over (−∞,∞) with an equal mesh size and proposed in 1974 x = φ(t) = tanh( 2 sinh t) as an optimal choice of variable transform...

Sufficient conditions to guarantee the existence and global exponential stability of periodic solutions of a CohenGrossberg-type BAM neural network are established by suitable mathematical transformation.

A bilinear Bäcklund transformation is presented for a (3 + 1)-dimensional generalized KP equation, which consists of six bilinear equations and involves nine arbitrary parameters. Two classes of exponential and rational traveling wave solutions with arbitrary wave numbers are computed, based on the proposed bilinear Bäcklund transformation. Published by Elsevier Ltd

As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet ...

Abstract: The paper is concerned with the existence and global exponential stability of periodic solutions for inertial Cohen-Grossberg-type BAM neural networks with time delays. With variable transformation the system is transformed to first order differential equations. Some new sufficient conditions ensuring the existence and global exponential stability of periodic solutions for the system ...

Let R be an o-minimal expansion of the field of real numbers that defines nontrivial arcs of both the sine and exponential functions. Let G be a collection of images of solutions on intervals to differential equations y′ = F (y), where F ranges over all R-linear transformations R → R. Then either the expansion of R by the elements of G is as well behaved relative to R as one could reasonably ho...

We generalize the Toda lattice (or Toda chain) equation to the square lattice, i.e., we construct an integrable nonlinear equation for a scalar field taking values on the square lattice and depending on a continuous (time) variable, characterized by an exponential law of interaction in both discrete directions of the square lattice. We construct the Darboux-Bäcklund transformations for such lat...